Here is the full list of all 19 War in a Box: Paper Tanks achievements.
Finish the level with 1 life
Lose 3 rounds in a row
Built 100 CANNONS
Built 20 TESLAS
Destroy 50 units using TESLA
Collect 50 stars
Collect 65 stars
Finish the game in Expert mode
Kill heavy tank or zeppelin with HEAVY-GUN
Win 10 rounds in a row
Built 25 ARTILLERY
Built 25 HEAVY-GUNS
Destroy 300 units using ARTILLERY
Destroy 1000 units using FLACK
Destroy 300 units using HEAVY-GUN
Collect 35 stars
Built 25 FLACKS
Destroy 1000 units using CANNON
Granted for first kill